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%I #19 Aug 19 2022 02:24:59
%S 1,1,1,1,5,21,61,211,1401,8065,37241,240021,1997821,13856701,94418325,
%T 874328911,8304303281,69158458881,658339599601,7454839614985,
%U 78224066633781,805961931388741,9828080719704941,124199805022959051,1466207770078872745
%N Expansion of e.g.f. exp( x * exp(x^3/6) ).
%C This sequence is different from A143567.
%H Seiichi Manyama, <a href="/A354551/b354551.txt">Table of n, a(n) for n = 0..523</a>
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * k! * (n - 3*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)))))
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*k!*(n-3*k)!));
%Y Cf. A000248, A354550, A354552.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Aug 18 2022